Global existence for nonlinear parabolic equations (Q1082537)

On \({\mathbb{R}}^ n\times (0,\infty)\), the existence and decay estimates of the initial value problem for a parabolic equation with the heat operator and a general nonlinear term, is considered. Using the Nash-Moser- Hörmander iterative scheme combined with decay estimates for the solution of the linearized parabolic equation, the authors improve an earlier result of Klainerman to a best possible one. An extremely clear writing is an additional attribute of this paper.